From the passenger terminal walk through the tunnel, walk until you see a big roundabout. There is a bus stop immediately before. Ideal hitching spot, cars are coming slowly and they have plenty of space to stop.
Perfect spot if you want to go south (London, or directly Heathrow Airport). Balazs did not test other directions, possibly works northwards too.
Candlewick took the free shuttle bus to the long term car park, get off at the first stop within the car park, and walk back towards the airport signing, I got a lift half way back. If not, you've made your way to the bus stop mentioned above. Good to try and catch drivers of airport workers.
Accommodation and Sleep
There are some double seats in the arrivals terminal, on which you can sleep. There is no free wifi and tap water is hot. (You can drink it, but you have to put it in bottles and wait for it to cool down)
Other useful info
There is an ASDA hypermarket around 2kms north from the airport. Check on Google Maps or ask airport staff. If you have time, and planning to spend the night in the airport, it is worth going there and buy food for yourself at the fraction of the price.